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Volume 20
Issue 3
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Math. Comput. Appl., Volume 20, Issue 3 (December 2015) – 6 articles , Pages 151-227

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811 KiB  
Article
Study on Water Seepage Law of Raw Coal During Loading Process
by Meng Junqing and Nie Baisheng
Math. Comput. Appl. 2015, 20(3), 217-227; https://doi.org/10.3390/mca20010227 - 1 Dec 2015
Viewed by 1677
Abstract
In order to reveal the water seepage law of raw coal during different loading process, the gravity constant load seepage experimental system is developed and used in this paper. The water seepage law of raw coal during different loading process was tested. The [...] Read more.
In order to reveal the water seepage law of raw coal during different loading process, the gravity constant load seepage experimental system is developed and used in this paper. The water seepage law of raw coal during different loading process was tested. The mathematical model of axial strain-damage-permeability coefficient during the loading process is proposed based on the Wei-bull distribution of coal damage. According to the water seepage experiments and results analysis, the following conclusions are gotten. Under the same experimental conditions, with the increasing of axial pressure, the permeability coefficient of coal sample has a distinct decrease trend, and then an increase trend when reached the extreme point. The same trend of permeability coefficient-strain curves and stress-strain curve of the raw coal samples under different axial pressure are got-ten, that mean the permeability coefficient is closely related to the damage evolution process. The water seepage law of raw coal during different loading process can be described by the mathematical model of axial strain-damage-permeability coefficient, and its parameters can be obtained easily. This research is important for revealing the mechanism of coal seam water seepage, guiding field coal seam water infusion, controlling mine water hazard, preventing coal mine disasters. Full article
690 KiB  
Article
Stability and Bifurcation Analysis of a Pipe Conveying Pulsating Fluid with Combination Parametric and Internal Resonances
by Liangqiang Zhou, Fangqi Chen and Yushu Chen
Math. Comput. Appl. 2015, 20(3), 200-216; https://doi.org/10.3390/mca20010216 - 1 Dec 2015
Cited by 2 | Viewed by 1784
Abstract
The stability and bifurcations of a hinged-hinged pipe conveying pulsating fluid with combination parametric and internal resonances are studied with both analytical and numerical methods. The system has geometric cubic nonlinearity. Three types of critical points for the bifurcation response equations are considered. [...] Read more.
The stability and bifurcations of a hinged-hinged pipe conveying pulsating fluid with combination parametric and internal resonances are studied with both analytical and numerical methods. The system has geometric cubic nonlinearity. Three types of critical points for the bifurcation response equations are considered. These points are characterized by a double zero and two negative eigenvalues, double zero and a pair of purely imaginary eigenvalues, and two pairs of purely imaginary eigenvalues, respectively. With the aid of normal form theory, the expressions for the critical bifurcation lines leading to incipient and secondary bifurcations are obtained. Possible bifurcations leading to 2-D tori are also investigated. Numerical simulations confirm the analytical results. Full article
430 KiB  
Article
Multiple Attribute Decision-Making Model of Grey Target Based on Positive and Negative Bull's-Eye
by Sha Fu
Math. Comput. Appl. 2015, 20(3), 189-199; https://doi.org/10.3390/mca20010199 - 1 Dec 2015
Viewed by 1653
Abstract
Aiming at complexity and uncertainty of actual decision-making environment, this study proposes a multiple attribute decision-making model of grey target based on positive and negative bull’s-eye. Firstly, it defines that the optimal effect vector and the worst effect vector of grey target decision [...] Read more.
Aiming at complexity and uncertainty of actual decision-making environment, this study proposes a multiple attribute decision-making model of grey target based on positive and negative bull’s-eye. Firstly, it defines that the optimal effect vector and the worst effect vector of grey target decision are respectively positive, negative bull’s-eye of the grey target; secondly, comprehensively considering the space projection distance between various schemes and the positive and negative bull’s-eye, it takes bull’s-eye distance as the basis for space analysis and obtains a new integrated bull’s-eye distance; then, in accordance with the comprehensive guidelines to minimize the bull’s-eye distance, it constructs goal programming model for goal function, and thus solves the index weight. Finally, through case studies of selective purchase of information system, it verifies feasibility and effectiveness of the proposed grey target decision-making model. Full article
790 KiB  
Article
Spinning Flow of Casson Fluid near an Infinite Rotating Disk
by Najeeb Alam Khan and Zehra Husain
Math. Comput. Appl. 2015, 20(3), 174-188; https://doi.org/10.3390/mca20010188 - 1 Dec 2015
Cited by 1 | Viewed by 1375
Abstract
This paper presents an investigation of the spinning flow of a non-Newtonian Casson fluid over a rotating disk. The model established for the governing problem in the form of partial differential equations has been converted to ordinary differential equations with the use of [...] Read more.
This paper presents an investigation of the spinning flow of a non-Newtonian Casson fluid over a rotating disk. The model established for the governing problem in the form of partial differential equations has been converted to ordinary differential equations with the use of suitable similarity transformation. The analytical approximation has been made with the most likely analytical method, homotopy analysis method (HAM). The convergence region of the obtained solution is determined and plotted. The velocity profiles are shown and the influence of Casson parameter is discussed in detail. Also comparison has been made with the Newtonian fluid as the special case of considered problem. Full article
772 KiB  
Article
Bernstein Collocation Method for Solving the First Order Nonlinear Differential Equations with the Mixed Non-Linear Conditions
by Salih Yalçınbaş and Huriye Gürler
Math. Comput. Appl. 2015, 20(3), 160-173; https://doi.org/10.3390/mca20010173 - 1 Dec 2015
Cited by 1 | Viewed by 1481
Abstract
In this study, we present the Bernstein matrix method to solve the first order nonlinear ordinary differential equations with the mixed non-linear conditions. By using this method, we obtain the approximate solutions in form of the Bernstein polynomials [1,2,16,17]. The method reduces the [...] Read more.
In this study, we present the Bernstein matrix method to solve the first order nonlinear ordinary differential equations with the mixed non-linear conditions. By using this method, we obtain the approximate solutions in form of the Bernstein polynomials [1,2,16,17]. The method reduces the problem to a system of the nonlinear algebraic equations by means of the required matrix relations of the solutions form. By solving this system, the approximate solution is obtained. Finally, the method will be illustrated on the examples. Full article
310 KiB  
Article
Derivation of a Six-Step Block Method for Direct Solution of Second Order Ordinary Differential Equations
by J. O. Kuboye and Z. Omar
Math. Comput. Appl. 2015, 20(3), 151-159; https://doi.org/10.3390/mca20010159 - 1 Dec 2015
Viewed by 1818
Abstract
A new six-step block method for solving second order initial value problems of ordinary differential equations is proposed using interpolation and collocation strategies. In developing this method, the power series adopted as an approximate solution is employed as interpolation equation while its second [...] Read more.
A new six-step block method for solving second order initial value problems of ordinary differential equations is proposed using interpolation and collocation strategies. In developing this method, the power series adopted as an approximate solution is employed as interpolation equation while its second derivative is used as collocation equation. In addition, the stability properties of the developed method are also established. The numerical results reveal that the new method produces better accuracy if compared to existing methods when solving the same problems. Full article
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